A new shrinkage estimator in negative binomial regression model

Studies have proven that the ridge estimator proves itself as a highly desirable shrinkage tool for addressing multicollinearity issues. A widely used model called negative binomial regression model (NBRM functions efficiently when count data contains overdispersion properties. Maximum likelihood estimator (MLE) produces coefficients whose variance becomes affected negatively by multicollinearity issues. The proposed paper introduces the generalized ridge estimator to resolve the shortcomings of ridge estimator. Various approaches to estimate the shrinkage matrix have been developed. Monte Carlo simulation findings demonstrate that the proposed estimation technique produces superior MSE results than traditional MLE estimates and ridge estimates regardless of the selected shrinkage matrix estimation methodology. The estimating methods used for shrinkage matrices result in different levels of performance enhancement.